Question

Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?

Answer 1

Answer:

a) Rs 603.68

b) Rs 476.33

c) first division

Step-by-step explanation:

Total profit = profit 1 + profit 2 = P

hence P ~ N(12,74) = $\frac{P-12}{\sqrt{74} } ~ N(0,1)$

A ) Specifying a Rupee range ( centered on the mean ) that contains 95% probability for annual profit of the company

$13.41 = Rs 603.68

B) specifying the 5th percentile of profit

p = $10.59 ≈ Rs 476.33

C) The  division that has a larger probability of making a loss in a given year is the first division

attached below is a detailed solution of the given problem